Research article

The molecular basis of the effect of temperature on enzyme activity

Roy M. Daniel, Michelle E. Peterson, Michael J. Danson, Nicholas C. Price, Sharon M. Kelly, Colin R. Monk, Cristina S. Weinberg, Matthew L. Oudshoorn, Charles K. Lee


Experimental data show that the effect of temperature on enzymes cannot be adequately explained in terms of a two-state model based on increases in activity and denaturation. The Equilibrium Model provides a quantitative explanation of enzyme thermal behaviour under reaction conditions by introducing an inactive (but not denatured) intermediate in rapid equilibrium with the active form. The temperature midpoint (Teq) of the rapid equilibration between the two forms is related to the growth temperature of the organism, and the enthalpy of the equilibrium (ΔHeq) to its ability to function over various temperature ranges. In the present study, we show that the difference between the active and inactive forms is at the enzyme active site. The results reveal an apparently universal mechanism, independent of enzyme reaction or structure, based at or near the active site, by which enzymes lose activity as temperature rises, as opposed to denaturation which is global. Results show that activity losses below Teq may lead to significant errors in the determination of ΔG*cat made on the basis of the two-state (‘Classical’) model, and the measured kcat will then not be a true indication of an enzyme's catalytic power. Overall, the results provide a molecular rationale for observations that the active site tends to be more flexible than the enzyme as a whole, and that activity losses precede denaturation, and provide a general explanation in molecular terms for the effect of temperature on enzyme activity.

  • adaptation
  • enzyme
  • Equilibrium Model
  • evolution
  • kinetics
  • temperature


The way enzymes respond to temperature is fundamental to many areas of biology. Until recently, the effect of temperature on enzyme activity has been understood in terms of raised temperature increasing activity and, at the same time, causing activity to be lost by denaturation (e.g. [13]). However, it is now clear that these two opposing effects are insufficient to explain the effect of temperature, and that the effect of temperature on enzymes over time cannot be predicted from the ΔG*cat (activation energy of the catalysed reaction) and ΔG*inact (activation energy of the thermal inactivation process) of the enzyme ([4], but see [5], [6], but see [7], [8]). The Equilibrium Model ([4], but see [5], [6], but see [7]) has provided a quantitative explanation of enzyme thermal behaviour by introducing an intermediate inactive (but not denatured) form that is in rapid equilibrium with the active form. Embedded Image where Eact is the active form of the enzyme, which is in equilibrium with the inactive form, Einact; Keq is the equilibrium constant describing the ratio of Einact/Eact; kinact is the rate constant for the Einact to X reaction; and X is the irreversibly denatured form of the enzyme.

Table 1 shows a variety of enzymes for which Equilibrium Model parameters have been determined; all fitted the Model. The enzymes cover most reaction classes and could all be measured directly and continuously, ensuring rapid and accurate collection of Vmax data. It is apparent from the range of structures, from monomeric to hexameric, and including a citrate synthase where the active site is at a subunit interface ([6], but see [7], [914]), that conformity with the Equilibrium Model is apparently independent of quaternary structure as well as the reaction concerned. The data suggest that the Equilibrium Model is universally applicable to all enzymes where Vmax data can be obtained.

View this table:
Table 1 Thermodynamic parameters for 28 enzymes fitted to the Equilibrium Model

The parameters of all enzymes were derived by fitting assay data to the Equilibrium Model and thus relate to active enzymes in the presence of substrate and cofactor. The exceptions are the growth temperature optima (Tgrowth) of the source organism, which are cited from various sources [9] and are included here only to give a broad approximation of the expected ‘working’ temperature of the enzyme. AAA, aryl acylamidase; ACP, acid phosphatase; AKP, alkaline phosphatase; DHFR, dihydrofolate reductase; GCS, citrate (si)-synthase; GGT, γ-glutamyltransferase; IPMDH, isopropylmalate dehydrogenase; PAL, phenylalanine ammonia lyase.

Using the Equilibrium Model, the variation of enzyme activity with temperature can be expressed by: Embedded Image with Embedded Image and Embedded Image where kcat is the enzyme catalytic rate constant, t is the assay duration, E0 is the enzyme concentration, ΔHeq is the change in enthalpy associated with the Eact/Einact equilibrium, Teq is the temperature midpoint of the Eact/Einact equilibrium, kB is Boltzmann's constant, R is the gas constant, T is temperature, and h is Planck's constant.

The experimental data (Figure 1A) fit the Equilibrium Model (Figure 1B), but not a simpler two-state model that only considers ΔG*cat and ΔG*inact (the ‘Classical Model’, Figure 1C). The new parameters associated with the model provide tools for understanding and quantifying the temperature-dependence of enzyme activity and the adaptation of enzymes and organisms to temperature, and to ranges of temperature. Teq, the temperature of the midpoint of the equilibrium between the active and reversibly inactive forms of the enzyme, is an evolved property of enzymes related to the organism's growth temperature, being more closely correlated with the environmental temperature of the enzyme than is its stability [9]. ΔHeq, the enthalpic change associated with the equilibrium, governs the temperature range over which the equilibrium occurs and thus the ability of the enzyme to function at different temperatures and temperature ranges [9].

Figure 1 Comparison of experimental data with the predictions of the Equilibrium and Classical Models: the effect of temperature on β-glucosidase from C. saccharolyticus with 30 mM p-nitrophenyl β-D-glucopyranoside as substrate

(A) Experimental data. (B) Simulation of the effect of temperature using parameters derived from fitting the experimental data to the Equilibrium Model (ΔG*cat=78 kJ·mol−1; ΔG*inact=105 kJ·mol−1; ΔHeq=119 kJ·mol−1; Teq=72 °C). (C) Simulation of the effect of temperature using only the values of ΔG*cat and ΔG*inact from fitting the experimental data to the Classical Model.

The Equilibrium Model quantitatively explains the effect of temperature on all enzymes for which Vmax can be measured over a range of temperatures ([4], but see [5], [6], but see [7], [9,1113,15,16]) and has predicted and explained the counterintuitive behaviour of enzyme reactors at some temperatures ([15], and M.L. Oudshoorn and R.M. Daniel, unpublished work). We cannot exclude the possibility that more complex models for the dependence of enzyme activity will fit experimental data, but none has been demonstrated.

The Equilibrium Model in itself does not offer an explanation of the molecular basis of these effects, or the physical nature of Einact. In the present study, we provide evidence that the difference between the active and inactive forms is at the enzyme active site, and confirm that Keq and its components Teq and ΔHeq are independent of global stability. This enables a general explanation in molecular terms for the effect of temperature on enzyme activity and reveals a new structurally localized and apparently universal mechanism for enzyme activity loss with increasing temperature, additional to denaturation.


Continuous enzyme assays

Continuous spectrophotometric enzyme assays were carried out as described previously [9,14,16] using a Thermo Spectronic Helios γ-spectrophotometer equipped with a Thermo Spectronic single-cell Peltier-effect cuvette holder. Assays were performed across a suitable range of temperatures for each enzyme, and spectrophotometric data were collected at 0.5 or 1 s intervals for 3–5 min using Vision32 (version 1.25; Thermo Spectronic) on a Windows XP PC connected to the spectrophotometer.

All reactions were started by adding rapidly no more than 10 μl of enzyme solution (kept at 0 °C) to ≤1000 μl of temperature-equilibrated reaction mixture (containing substrate/cofactor and reaction buffer) in a quartz cuvette. Data collection started within 3 s of enzyme addition, and the temperature of the reaction remained within ±1 °C of the desired temperature. Where possible, substrate concentrations were set to at least ten times Km to approach Vmax; where it was not possible to do so (e.g. high Km or poor substrate solubility), Km values were determined and used to compensate for the deviation from Vmax. Blank rates were measured and used to correct reaction rates if necessary. All criteria required for accurate and valid determination of Equilibrium Model parameters [14] were met.

All enzymes shown in Table 1 have been assayed directly and continuously to allow rapid and accurate data collection and temperature control.

Bacillus subtilis subtilisin A (catalogue number P5380; Sigma–Aldrich) was assayed in 50 mM phosphate buffer (pH 7.3) using the following substrates (purchased from Bachem AG) (where E0 is enzyme concentration): 10 mM succinyl-Ala-Ala-Pro-Ala-p-nitroanilide (E0=118 nM); succinyl-Ala-Ala-Pro-Leu-p-nitroanilide (7 mM at 60–65 °C, 10 mM at 70–75 °C, 15 mM at 80–85 °C; E0=4.53 nM); 10 mM succinyl-Ala-Ala-Pro-Phep-nitroanilide (E0=2.28 nM); 10 mM succinyl-Ala-Ala-Pro-Nle-p-nitroanilide (E0=3.37 nM; Nle is norleucine); succinyl-Ala-Ala-Pro-Val-p-nitroanilide (25 mM at 30–70 °C, 50 mM at 75–85 °C; E0=337 nM). The assay volume was 400 μl in a quartz cuvette of 2 mm pathlength. Enzyme activity was measured by monitoring the production of p-nitroaniline at 400 nm (ε=9290 M−1·cm−1).

Caldicellulosiruptor saccharolyticus β-glucosidase, expressed recombinantly in Escherichia coli, was purified using chromatography following heat treatment [17]. It was assayed as described previously [9] using various substrates (purchased from Sigma–Aldrich), including 30 mM p-nitrophenyl β-D-glucopyranoside, 20 mM p-nitrophenyl β-D-galactopyranoside, 20 mM p-nitrophenyl β-D-fucopyranoside and 52 mM p-nitrophenyl β-D-xylopyranoside. For reaction buffer, 50 mM sodium phosphate buffer (pH 6.3) was used, and the concentration of enzyme in the assay was 0.586 μM for all substrates except for p-nitrophenyl β-D-xylopyranoside, which was 2.93 μM. The assay volume was 400 μl in a quartz cuvette of 2 mm pathlength. Enzyme activity was measured by monitoring the production of p-nitrophenol at 410 nm (ε=7930 M−1·cm−1).

Bos taurus GDH (glutamate dehydrogenase) (L-glutamic dehydrogenase from bovine liver; catalogue number G7882; Sigma–Aldrich) was assayed in 90 mM phosphate buffer (pH 7.3), with 0.05 mM EDTA, 160 mM ammonium acetate, 10 mM 2-oxoglutarate and 0.5 mM NADPH or NADH. The assay volume was 1 ml in a 10 mm pathlength quartz cuvette; enzyme activity was measured by monitoring absorbance at 340 nm (ε=6220 M−1·cm−1).

Bacillus sp. strain AK1 protease was cloned and expressed in E. coli; cells were harvested and lysed by sonication, and the enzyme was purified using phenyl-Sepharose [18]. The enzyme was assayed in 100 mM Hepes/NaOH with 5 mM CaCl2 (pH 7.5), using 22.5 mM succinyl-Ala-Ala-Ala-p-nitroanilide and 50 mM succinyl-Ala-Ala-Pro-Phe-p-nitroanilide. The assay volume was 400 μl in a quartz cuvette of 2 mm pathlength. The final enzyme concentration was 30.4 nM. Enzyme activity was measured by monitoring the production of p-nitroaniline at 410 nm (ε=7930 M−1·cm−1). The enzyme was pre-treated by incubation in buffer in the absence and presence of 10 mM DTT (dithiothreitol) for 60 min at room temperature (20 °C), then diluted 1:1 before adding to the reaction mixture.

Data processing

The processing of enzyme assay data was performed as described in detail in [14] using the MATLAB-based Equilibrium Model data-processing application on a CD-ROM (available on request from R.M.D.). In short, absorbance data from Vision32 were first converted into progress curves of product concentration (M) against time (s) in Excel, which were then loaded into the Equilibrium Model application, which performs the facile derivation of Equilibrium Model parameters from the experimental data. The application employs a fitting algorithm based on a least squares approximation run over multiple iterations to identify a set of thermodynamic parameters that best describe the experimental data within the confines of the Equilibrium Model. The resulting parameters were used to generate a simulated three-dimensional plot of enzyme activity profile (activity against temperature against time) that is then compared with the corresponding three-dimensional plot generated from smoothed raw assay data to ensure the validity of the final Equilibrium Model parameters. The values in parentheses in the Tables are the S.D. of the fit of the data to the model [14].

Circular dichroism

Saccharomyces cerevisiae α-glucosidase (E-SUCR; Megazyme International) was chosen for its prominent CD responses in the near-UV spectrum, which in turn are caused by the distinct characteristics of tryptophan residues, especially those near its active site (results not shown); however, it should be noted that the CD spectrum cannot be considered a quantitative measure of the overall conformation of the enzyme. CD time-course observations were performed at 292 nm, the wavelength at which the CD signal is maximal. Time-course experiments and CD spectral scans performed in the presence of substrate (i.e. under assay conditions) were carried out using 0.5 mg·ml−1 S. cerevisiae α-glucosidase in the presence of 300 mM maltose (SigmaUltra, catalogue number M9171; Sigma–Aldrich). A high concentration of maltose was used to avoid significant substrate depletion during measurement and thus to mirror the conditions used for the collection of Equilibrium Model data. Neither maltose nor its product glucose absorb significantly in the near UV range, regardless of temperature (results not shown). The buffer used was 20 mM sodium phosphate buffer (pH 7.5), and the total volume for each reaction was 2 ml. All CD measurements were made using a quartz cuvette of 10 mm pathlength. For CD spectral data, approx. 60 s passed between enzyme addition and the completion of the CD spectral scan. For CD time-course experiments, data recording started immediately (i.e. within 6 s) after enzyme was added to a pre-temperature-equilibrated reaction mixture.

S. cerevisiae α-glucosidase (4.84 nM) was assayed discontinuously using 300 mM maltose as substrate in 18 mM phosphate buffer (pH 7.0). Aliquots (100 μl) of the reaction were transferred at desired intervals to screw-capped tubes containing 100 μl of 50 mM phosphate buffer (pH 7.0) at 100 °C. The tubes were capped and placed in a water bath at 100 °C for 7 min to terminate the α-glucosidase reaction, and then transferred to an ice-water bath until samples for the full time course had been collected (8.5 min at 30 s intervals). To each 200 μl of stopped reaction mixture, 3 units of glucose dehydrogenase (catalogue number G5059; Sigma–Aldrich) and β-NADP+ to a final concentration of 4.5 mM were added and incubated at 35 °C for 35 min. The concentrations of NADPH were calculated from absorbance data at 340 nm (5 mm pathlength cuvette).


Eact/Einact transition timescale

The timescale for the Eact/Einact equilibration is clearly rapid, since all the variation of activity at zero time {e.g. Figure 1A; ([4], but see [5], [6], but see [7])} occurs as a result of changes in the Eact/Einact equilibrium, and is thus attained over timescales shorter than the mixing process, probably <2 s. The implication is that for every enzyme tested (Table 1) the Eact/Einact equilibration timescale is of this order or shorter, whereas most proteins take very much longer than this to unfold [19,20]. This is particularly the case given the relatively low temperatures at which some Eact/Einact equilibrations take place. The results shown in Table 1 demonstrate that many enzymes are only partially active at physiological temperatures, depending on the value of ΔHeq. For enzymes with low ΔHeq values, the Eact into Einact conversion takes place over a broad temperature range, beginning at relatively low temperatures. For example, 10% of the Prunus dulcis β-glucosidase enzyme (ΔHeq=100 kJ·mol−1) is already in the Einact form at 36 °C. On the other hand, for E. coli MDH (malate dehydrogenase) (ΔHeq=619 kJ·mol−1), 10% Einact is not reached until 67 °C (see Figure 6).

Magnitude of ΔHeq

The enthalpic change associated with the Eact/Einact equilibrium, ΔHeq, is much smaller than that associated with denaturation (ΔHunfold) per amino acid residue. For example, the ΔHeq for subtilisin at 60 °C (i.e. at Teq) is approx. 110 kJ·mol−1 (Table 2), whereas the ΔHunfold at this temperature has been determined to be approx. 1350 kJ·mol−1 [21]. For ten single-subunit enzymes with Teq values between 53 and 75 °C, the average ΔHeq is 0.47±0.40 kJ·mol−1·residue−1 (range 0.08–1.51 kJ·mol−1·residue−1). Similar values apply to multi-subunit enzymes. An estimate for the average ΔHunfold in this temperature range is 3.0–4.3 kJ·mol−1·residue−1 [22,23]. Although this is, at best, an approximation, it confirms that the expected ΔHunfold for these enzymes is about one order of magnitude greater than their ΔHeq.

View this table:
Table 2 Effect of substrate on the Equilibrium Model parameters of three enzymes

Enzymes were assayed using different substrates and the Equilibrium Model parameters derived as outlined in Experimental. Data are presented to three significant figures. Values in parentheses are the S.D. of the fit of the data to the Model.

Structural studies

We have used CD to probe the extent and timing of the structural changes associated with the Eact/Einact equilibrium and with denaturation in the α-glucosidase from S. cerevisiae under assay conditions. Near-UV CD spectral features specific to the native (non-denatured) enzyme were observed at 15 °C in the presence of 300 mM maltose (Figure 2, continuous line), whereas at 43 °C in the absence of substrate (i.e. non-Equilibrium Model condition), where the enzyme is denatured, no distinct features can be seen (Figure 2, broken line). Similar observations were made from CD time-course experiments monitoring CD signals at 292 nm (Figure 3). At 15 °C in the presence of substrate, the initial CD signal of the enzyme at 292 nm is very similar to the value seen in Figure 2 (Figure 3, dashed line) and changes only slightly over the duration of the experiment (25 min); this is expected since under such conditions the enzyme exists mostly in its active form ([Eact]>99.95%) and undergoes very limited denaturation. In contrast, at 43 °C in the absence of substrate, the CD signal at 292 nm decreases quickly (Figure 3, dotted line) and irreversibly (results not shown), reflecting both the absence of any stabilizing effect of substrate, and the buffering effect of the Eact/Einact equilibrium against denaturation ([4], but see [5], [13]). The initial CD signal under this condition is also considerably lower than that at 43 °C in the presence of substrate (Figure 3, continuous line), where approx. 50% of the enzyme exists as Einact and where the initial CD signal is itself significantly reduced compared with that at 15 °C (Figure 3, dashed line). Furthermore, the decrease in CD signal at 43 °C in the presence of substrate over the course of the experiment is comparable with the rate of enzyme denaturation in the assay (see Figure 4).

Figure 2 CD spectra of S. cerevisiae α-glucosidase

S. cerevisiae α-glucosidase was scanned at 15 °C in the presence of 300 mM maltose (continuous line) and, after a 10-min incubation at 43 °C, in the absence of substrate (broken line).

Figure 3 Time-dependent changes in CD signals at 292 nm of S. cerevisiae α-glucosidase

S. cerevisiae α-glucosidase CD time-course experiments were performed at 15 °C in the presence of 300 mM maltose (dashed line), at 43 °C in the presence of 300 mM maltose (continuous line), at 43 °C in the absence of substrate (dotted line), and after a 30-min incubation at 43 °C following the time-course experiment at 43 °C in the presence of 300 mM maltose (dashed-dotted line).

Figure 4 An experimental time–temperature–activity plot of the S. cerevisiae α-glucosidase

ΔG*cat=63.5 kJ·mol−1; ΔG*inact=96.9 kJ·mol−1; ΔHeq=215 kJ·mol−1; Teq=316.5K.

CD time-course experiments suggest that the changes in tertiary structure occur in at least two stages, over different timescales. The first stage (the Eact/Einact transition) can be seen in the difference between the initial CD signals at 15 and 43 °C in the presence of substrate (Figure 3, dashed and continuous lines respectively), which corresponds to a shift from ~100% Eact (15 °C) to approx. 50% Eact and 50% Einact (43 °C); this shift is rapid since the time course was started at near zero time, i.e. within 6 s of addition of the enzyme to substrates and buffer. The second and time-dependent change is thermal denaturation, which occurs at a rate comparable with that of the conversion from Einact into X (Figure 3, continuous and dashed-dotted lines, and Figure 4, changes along the rate/time axes at 43 °C) and is lower than the rate of decrease in the absence of substrate (Figure 3, dotted line). Furthermore, one enzyme/substrate mixture was incubated at 43 °C for an additional 30 min after the time-course experiment and monitored again for another 25 min (Figure 3, dashed-dotted line), after which its CD signal is essentially identical with that of the fully denatured enzyme (Figure 3, dotted line). It is likely that the enzyme denatured fully during the extended incubation and exists solely as the denatured form.

Substrate effects

Teq and ΔHeq are substrate-specific, i.e. different enzyme/substrate combinations have their own characteristic values of Teq and ΔHeq (Table 2). These are often markedly different from one another, with some relationship between the size of the differences in Teq and ΔHeq and the extent of the structural differences.

In the case of subtilisin, the effect is evident at the S1 site, since the only difference in the substrates is at the P1 position. The change from leucine to norleucine at the P1 position of the substrate has relatively little effect on ΔG*cat or ΔG*inact, but marked changes can be seen for Teq and ΔHeq; the change from norleucine to alanine does not significantly affect stability, but there are major differences in Teq and ΔHeq as well as in ΔG*cat. For phenylalanine, the stability and the Teq are the same as for valine, but the ΔHeq is higher than for any of the other substrates.

For β-glucosidase, the effect of the 6-deoxyhexose fucose is to lower stability and raise Teq and ΔHeq compared with the aldohexose substrates galactose and glucose. These two have the same Teq and similar stabilities. The pentose substrate xylose substantially lowers Teq, while maintaining high stability.

In the case of GDH, cofactors affect Teq and ΔHeq in the same way as substrates, with substantial differences in the absence of any significant effect on ΔG*cat or ΔG*inact.

Km changes often coincide with the Eact/Einact transition. There have been a number of general observations that enzyme Km values often increase with temperature [24]. We find that these increases are relatively common and often coincide with the shift from Eact to Einact. For example, Figure 5 shows the sharp increase in the Km of MDH for oxaloacetate coincident with a sudden increase in the proportion of Einact, and a slower increase in Km of GDH for NADPH coincident with an increase in Einact spread over a larger temperature range.

Figure 5 Effects of temperature on the Eact/Einact equilibrium and Km

The continuous lines represent the initial (zero time) activity of the enzyme at various temperatures based on its Equilibrium Model parameters derived from experimental data. The percentages refer to the proportion of Einact relative to the total enzyme population at temperatures indicated by arrows. The broken lines represent the effect of temperature on the Km of the enzyme (means±S.E.M.). (A) E. coli MDH; Km values are for oxaloacetate. (B) Alvinella pompejana epibionts GDH; Km values are for NADPH.

An active-site change affects Teq

The AK1 protease is unusual in that it has a disulfide bond in the active site, between Cys137 and Cys139. Cleavage of this bond has a significant impact on the active site, since residues 133–136 form a promontory that projects between the S1 and S4 sites, and the chain displacement arising from cleavage affects the Km and kcat values of the enzyme, depending upon the temperature and substrate [18,25]. As shown in Table 3, reductive cleavage of this disulfide bond using DTT results in significant changes in Teq and ΔHeq, without significant changes in ΔG*cat or ΔG*inact. This is found with both substrates used, showing that a point change at a well-defined position in the active site of an enzyme has an effect on the Equilibrium Model parameters describing the Eact/Einact equilibrium.

View this table:
Table 3 Effect of disulfide bond cleavage at the active site on the Equilibrium Model parameters of AK1 protease with two different peptide substrates

Data are presented to three significant figures. Values in parentheses are the S.D. of the fit of the data to the Model.

Effect of ΔHeq on the determination of ΔG*cat and kcat

In addition to the known effect of ΔHeq on the temperature range over which enzymes operate [9], Figure 6 shows that, for enzymes with a low ΔHeq, such as β-glucosidase, a significant proportion of the enzyme can be in the inactive form at temperatures well below Teq. This leads to a relatively straighter shape of the ascending limb of the temperature–activity curve for the P. dulcis β-glucosidase, because the effect of Teq is imposed upon that of ΔG*cat. In this case, attempts to determine ΔG*cat from a simple plot of the increase in activity with temperature for this enzyme will be open to significant errors, as will measurements of kcat if made over the affected temperature range.

Figure 6 Effect of ΔHeq on the temperature-sensitivity of enzymes via the Eact/Einact equilibrium

The continuous line shows the zero time activity of E. coli MDH (ΔHeq=619 kJ·mol−1), and the broken line shows that of P. dulcis β-glucosidase (ΔHeq=100 kJ·mol−1). The vertical arrows show the percentage of the enzyme existing as the inactive form.


A variety of evidence from the present study indicates that the Eact/Einact transition involves relatively little unfolding, and that Einact is not significantly denatured, i.e. the results show that the Einact form of an enzyme is relatively similar to the Eact form, rather than to the denatured/unfolded form, or to a molten globule form. The speed of the Eact/Einact equilibration is much greater than that of denaturation and consistent with the conformational switching time between the sub-states of the myoglobin-binding site [26]. The ΔHeq values are much lower than that expected for denaturation and are consistent with conformational changes, very limited unfolding and/or changes in solvent interactions. However, the range of values for ΔHeq, from less than 90 kJ·mol−1 to more than 800 kJ·mol−1, and less than 0.1 kJ·mol−1·residue−1 (e.g., B. taurus alkaline phosphatase and P. dulcis β-glucosidase) to more than 1.2 kJ·mol−1·residue−1 (B. cereus dihydrofolate reductase and B. taurus MDH) is large, and it seems likely that different events are involved in different enzymes. Earlier work has shown that a low concentration of a denaturing agent or stabilizing agent can affect temperature stability without affecting Teq and ΔHeq, also indicating that these parameters are independent of enzyme global stability [15]. A statistical analysis of a number of enzymes [9] has already shown a stronger correlation of the growth temperature of the source organism with Teq than with ΔG*inact (stability); the correlation of ΔG*inact with Teq is weaker and predictable given that both correlate with growth temperature. The CD data support the notion that the Eact/Einact transition occurs very rapidly compared with denaturation, is temperature-dependent and is physically distinct from the slower denaturation process. Overall, these findings provide an explanation for the results of Tsou [20,27] showing that thermally induced loss of enzyme activity occurs at lower temperatures and much more rapidly than denaturation [20,2729]. It may be that the change from Eact to Einact is the first, but very limited, step in a pathway leading to complete unfolding, but this is not a necessary consequence of these results.

Other evidence indicates that changes at the active site are responsible for the Eact/Einact equilibration. The parameters defining the transition, Teq and ΔHeq, are substrate-specific, with similar substrates often giving similar parameters for a given enzyme, and structurally different substrates giving rise to significant differences in the parameters, often without significant changes in ΔG*cat (succinyl-Ala-Ala-Pro-Leup-nitroanilide/succinyl-Ala-Ala-Pro-Nle-p-nitroanilide; p-nitrophenyl β-D-fucopyranoside/p-nitrophenyl β-D-galactopyranoside; NADH/NADPH) or ΔG*inact (succinyl-Ala-Ala-Pro-Leu-p-nitroanilide/succinyl-Ala-Ala-Pro-Nle-p-nitroanilide; succinylAla-Ala-Pro-Nle-p-nitroanilide/succinyl-Ala-Ala-Pro-Ala-p-nitroanilide; succinyl-Ala-Ala-Pro-Phe-p-ni-troanilide/succinyl-Ala-Ala-Pro-Val-p-nitroanilide; p-nitrophenyl β-D-glucopyranoside/p-nitrophenyl β-D-xylopyranoside) (Table 2).

A point change at the active site, in this case cleavage of a disulfide bond that produces insignificant changes in the global structure [25], but that gives rise to a structural change at the active site, can also produce changes in the parameters Teq and ΔHeq, providing direct evidence for involvement of the active site in Eact/Einact equilibration (Table 3). The general observation that Km tends to rise with temperature [24], and that these changes are often associated with shifts in the Eact/Einact equilibrium, are both consistent with changes at the active site from an optimum configuration for substrate binding to a less optimum one, coincident with a shift in the Eact/Einact equilibrium towards the Einact form. We would not expect this to be invariably the case, since, in some enzymes, shifts in the Eact/Einact equilibrium might depend on active-site residues that do not affect Km. Overall, the results show that the active sites of enzymes dictate the effect of temperature on enzyme activity. This is entirely consistent with, and may provide part of the rationale for, observations that the active site tends to be more flexible than the enzyme as a whole [20,2734]. The exact nature of the physical changes involved are not clear and, given the range of reactions and structures covered by the Equilibrium Model, seem likely to be different in different enzymes, but it would be very surprising if some type of conformational change was not involved.

The inference from Figure 6 is that, for enzymes with a low ΔHeq, such as the β-glucosidase shown, attempts to determine ΔG*cat graphically, without taking account of Teq, are likely to have significant errors. Any determination of kcat will only be a true measure of the enzyme's catalytic power if it is made at temperatures where none of the enzyme is in the inactive form. Since the average ΔHeq of the enzymes for which it has been determined is 226 kJ·mol−1, and 150 kJ·mol−1 for single-subunit enzymes (Table 1), this may often be at surprisingly low temperatures.

As discussed elsewhere [15], the Equilibrium Model has significant applications for the effects of temperature on enzyme evolution and adaptation [9,15,16]. The several-fold lower initial rate that is observed for the Equilibrium Model compared with the Classical Model (Figure 1) is a direct consequence of the values assigned to the thermodynamic parameters in the former, particularly the value of Teq being lower than the temperature bringing about significant irreversible thermal inactivation. The initial rate observed thus increases as the value of Teq is increased. This may help to explain why thermophilic enzymes only achieve catalytic rates equivalent to those found with mesophilic enzymes, despite the higher temperature of assay. That is, a thermophilic enzyme may have a high global stability that results in low rates of thermal inactivation, but the active-site structure may not be optimized for thermal stability but for effective catalysis, and thus of necessity may comprise a more flexible portion of the protein. As the temperature of the enzyme is raised, the flexible active-site region may be deformed and Eact thus converted into Einact with a concomitant reduction in catalytic activity. However, as the major portion of the protein molecule is optimized for stability and can act as a stable scaffold, the temperature-induced conformation change at the active site can be prevented from leading to total unfolding and the conversion of Eact into Einact is consequently reversible at potentially destabilizing temperatures. However, this effect does lead to lower catalytic rates and a lower Teq than would be expected from the optimum growth temperature of the organism.

The results imply that evolution of the enzyme active site is likely to be constrained by its temperature-dependence. Manipulation of stability by mutation, whether naturally or by directed mutagenesis, may not allow activity at higher temperatures unless Teq is also raised; since the basis of Eact/Einact equilibration is at the active site, this may lead to changes in Km and/or kcat. This may explain the difficulty of engineering enzymes to operate at higher temperatures.

Of particular interest is the discovery of a localized and apparently universal mechanism by which enzymes lose activity as temperature rises, as opposed to denaturation which is global [35]. The Einact state of the Equilibrium Model is clearly different from a fully unfolded or molten globule state and is thus distinguishable from the Lumry–Eyring model [36] and other models [15]. The molecular basis of any specific Eact/Einact equilibration seems likely to be as diverse as the enzymes themselves. The precise details of the local changes occurring in any specific enzyme as the equilibrium shifts from Eact to Einact have yet to be determined. This determination may not be simple since the structural difference between the two forms is evidently small, and the temperature required to yield a dominating proportion of Einact will cause rapid denaturation of most enzymes.

The applicability across such a wide range of enzyme reactions and structures, the active-site location, and the association with growth temperature [9] all strongly indicate that the Equilibrium Model describes an important natural phenomenon.


Roy Daniel and Michael Danson conceived the general hypothesis and, with Charles Lee, wrote the paper. Roy Daniel planned the experiments and interpreted the data. Michelle Petersen, Charles Lee, Cristina Weinberg, Matthew Oudshoorn and Colin Monk planned and carried out the experiments to determine the Equilibrium Model parameters and analysed the data. Colin Monk carried out much of the data processing and prepared the Figures. Nicholas Price and Charles Lee planned the CD experiments and interpreted the data. Sharon Kelly and Charles Lee carried out the CD experiments. All of the authors contributed to a critical review of the paper and approved the final version.


We thank the Royal Society of New Zealand Marsden Fund for financial support [grant number UOW0501].


We thank Alan Cooper for helpful discussions, and Martin Seefeld and Andreas Pickl for technical assistance.

Abbreviations: DTT, dithiothreitol; Eact, active enzyme; Einact, inactive enzyme; E0, enzyme concentration; GDH, glutamate dehydrogenase; MDH, malate dehydrogenase; Nle, norleucine; Teq, temperature at which the concentrations of Eact and Einact are equal


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